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Acceleration! by Tania Khan, Rebecca Kim and Jennifer Loh All You Need to Know About.

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1 Acceleration! by Tania Khan, Rebecca Kim and Jennifer Loh All You Need to Know About

2 What is acceleration? Acceleration is the quantity that describes the rate of change of velocity in a given time interval. The magnitude of the acceleration is calculated by using the formula: a = (v f – v i ) /( t f – t i ) An important fact to note is that acceleration does not change as a function of time. If an object's acceleration is 5 m/s 2, it stays at 5 m/s 2. (refer to winter break packet #42)

3 velocity vs. time graph

4 V vs. T graph explanation Lets say that a cart is in motion and its data is recorded as a graph. On the graph, when the line: a) goes up, the acceleration of the cart increases away from its starting point. b) stops and stays as a straight line, then the cart stops accelerating and the velocity of the cart stays constant while continuing to move away from its starting point. c) goes down, the cart decelerates but is still moving away from its starting point. d) goes down but its velocity turns negative, the cart begins to accelerate but towards its starting point. e) goes up but from the negative velocity point, the cart decelerates but moves away from its starting point.

5 Which car has the greatest acceleration during the time interval 10 seconds to 15 seconds? The answer to this problem is Car D because Car D's acceleration slope between 10 seconds to 15 seconds is the greatest compared to all the other cars which means that it has the greatest acceleration. Winter Packet #2

6 Finding Distance Using a V(T) Graph

7 Acceleration With Distance The general formula used to find distance when an object is in constant uniform acceleration is d = v i t - ½at 2. This formula is useful for finding the displacement of an object moving with uniform acceleration as well as finding the displacement required for an object to reach a certain speed or to come to a stop. The formula used to find distance when an object is in motion under the influence of gravity is d = v i t - ½gt 2. This formula is often used for free fall, where gravity is acting on the object.

8 Practice Problem A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s 2 for 15 s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to take off? Given: v i = 0 m/s a = 4.8 m/s 2 t = 15 s Find: v f = ? d = ?

9 Explanation to the Plane Problem v f = v i + at v f = 0 m/s + (4.8 m/s 2 )(15 s) v f = 72 m/s d = v i t + ½at 2 d = (0 m/s)(15 s) + ½(4.8 m/s 2 )(15 s) 2 d = 540 m

10 Calculating Acceleration When Time is not Given v f 2 = v i 2 + 2ad This equation comes in handy when the time interval is not mentioned in the problem. When using this equation, you have to take the square root of the whole right side of the equation to get the final velocity. The square root can either be positive or negative. But the sign can be determined based on the direction of the motion.

11 Let's do some practice!! Holt Physics Textbook page 57. A person pushing a stroller starts from rest, uniformly accelerating at a rate of m/s 2. What is the velocity of the stroller after it has traveled 4.75 m? Given: v i = 0 m/s * time is not given * a = m/s 2 d= 4.75 m

12 Answer v f 2 = (0 m/s) 2 + 2(0.500 m/s 2 ) (4.75m) v f 2 = 4.75 m 2 /s 2 v f =+/ m/s Since the stroller moves with a positive acceleration, the final velocity should be positive. v f = m/s

13 Video on Acceleration videos-playlist.htm#video G-force (or gravitational force) is an object's acceleration relative to free fall. The stress and strain on a person when they are accelerating at high speeds are accelerations that are not produced by gravity. This kind of acceleration is called proper acceleration. This type of acceleration, or g- force, is measured in g-force units. (Winter Packet #29)

14 HOMEWORK In midyear packet: #s 4, 12, 33, Holt: pg 53 #1, 2


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